What are your stats ? Montecarlosimulation of Trading / Moneymangement

Hi,

I was wondering who is of you is actually following their stats and using Montecarlo Simulation in order to choose their moneymangement properly and see if their strategy generates a constant profit? Yes, then what are your stats?

I was just running my excel sheet and I am currently running at the following stats

Pct winning trades: 37% (this is really low, but I'm trading on tight stops and the win/loss ratio makes it up)

Average Winning Trade / Average Losing trade: 2.06

Risk: ~ 5% of equity

In a 1000 iteration MC this looks as follows:

Simulation Results
Equity High 1588.15%
Equity Low -48.96%
Iterations 1000
Number of ruins 0 0.00% (currently defined as 50% loss of initial equity)

Not great, but at least no ruins. Thinking currently to up the stakes maybe to 6-7% risk.

Anybody who needs the excel sheet to perform the calculations, just drop me a PM.

I would be interested in your stats!

Cheers
Yuppie

Yuppie,

I guess you can see by your somewhat less than enthusiastic reception, the amount of thought most traders are giving to this. This is remarkable, because nothing effects your outcome more than money management (with the exception of psychology).

You state that there were '1000 iterations'. This is always an area of confusion to me. Does that mean you had 1000 trades per test, or simply one test with 1000 trades in it?

I suspect the latter, which is why you didn't get ruined in the simulation. It is my understanding that you have to do A LOT MORE than 1000 trades to get any meaningful results. Consider doing the simulation of 1000 trades 10,000 times, and looking at the worst of those results.

I ran your numbers on this webpage: http://www.automated-trading-system...calculation-tool/comment-page-1/#comment-1746 I have no idea how accurate the code is, but I have reason to believe it may be accurate.

I got ruined immediately with your leverage on 10,000 simulations. Even when I lowered the leverage to 1%, I found there was still nearly a 5% chance of hitting your Drawdown (ruin level). That's a 1 in 20 chance of being 'ruined' according to your definition.

Think you can handle those odds and want more leverage? Try 2% risk per trade. In 10,000 simulations you have ALMOST NO CHANCE of surviving (93.8% chance of 50% drawdown)

You are on the right track for sure considering position size. We just need better tools to do it. I'm still looking for a good MC simulator for studying this subject.

Another question that comes up is how do you know when enough is enough (sim count). If you do enough, your chances of hitting your drawdown keep increasing (your worst drawdown is always in the future). For example, with your system, I got a 4.9% chance of hitting your ruin level on 10,000 simulations. When I tried 1,000,000 simulations, the chances go up to 93.5%. So, the question becomes, what sim count is most reliable? Does it get to a point where it gets a little bit silly? Maybe a statistician can answer these questions.

I calculated your expectancy as .132R per trade. (This is expressed as a percentage of your risk per trade, 'R' being your risk.) This is how much money you won on average on your sample. Expressing reward and expectancy in terms of risk makes the most sense, rather than $43 per trade, etc. Then you can compare a 1 lot trader to a 100 lot trader, and have apples to apples.

BTW, how many trades in your sample. You can't even think about using less than 30. 100 is better. You may find Van Tharp's Book 'Super Trader' helpful since he talks a lot about money management.

Kind Regards,

fastcar

I have been wondering this about the rest of the traders here as well. I m deligted to see this post!! Currently I have made a "small" tweek in my system that seems to have exponentially increased my profit and expectancy but i do not have enough trades under my belt yet to give definite numbers. I would love to see your MC simulation. I have one but have felt that it is not that accurate. I will check out the site fastcar mentioned as well. I would love your Excel file to run my own numbers and be happy to report back after a few more months of this. If I can keep this up for the remainder of the year i should have enough data to really pour through.

By the way if you are risking 5% per trade this is probably a large part of why you are not feeling great about your system. Or is this 5% maximum at risk in ALL trades together (in keeping with the 2% and 6% rule that is commonly discussed)?

If you could send me a copy of that file I would greatly appreciate it.

Thanks in advance.

eegozi,

Don't forget to PM Yuppie in case he is not subscribed to this thread...

You can also try this download: http://www.box.net/shared/9ogdzi1epn It's free, but I could not get it to work properly on Excel 2011 for Mac.

Based on my limited experience doing Monte Carlo simulations, I think 5% on a system with a win rate as low as Yuppie's is a great way to blow up an account. What I'm starting to find out is that Expectancy is a poor measuring of a systems performance...

For example, you can have two systems with the same expectancy, and have HUGE differences in their optimal position sizing based on your risk tolerance (for example, you are willing to risk a DD of no more than 30%). Let me give you an example:

System 'A' has an expectancy of .2R, with a 60% win rate and a Win/Loss of 1:1. This system allows you to bet 1.5R per trade, and have just a 4.5% chance of touching a 30% DD in 10,000 simulations (see attachment).

Check out system 'B'. It has the SAME expectancy of .2R, but wins just 45% of the time. Now, when it wins, it wins DOUBLE what it risks. Almost sounds better than system 'A', doesn't it?

Well, of course, just looking at the Expectancy, you can see they are equal, but look what happens when you do a MC on them! Your chance of a 30% draw down on the second system jumps from 4.5% to 97.7%!!! This is bad news...

Now, in order to control risk on system 'B', you have to reduce position size by HALF, to .77% (from 1.5% per trade). Imagine what effect that will have on your returns!!!

This very moment I'm reading something I consider MUST READ for ANYONE interested in this subject. It is by Larry C. Sanders, it's free, and so far the first 5 pages have been very promising. He is touching right now on the limitations of Expectancy in a manner I was totally unaware of. He is also discussing the advantages of win rate for a give Expectancy. I'm very excited and amazed how much there is to this subject. Even after just 5 pages, I believe his paper promises more than what I have learned from Van Tharpe's work on the subject. I found Van Tharpe's 'Definitive Guide to Position Sizing' to be not so 'definitive' and more 'frustrating' as the reader is left with more questions than answers when through! Enjoy: http://www.tradelabstrategies.com/customers/tradingstrategiesrev2.pdf and please post any findings

fastcar

I run similar simulations on an ongoing basis, in order to try to work out statistical limits that I'm typically going to experience over the coming month. I tend to use resampling rather than true monte carlo

The Larry Sanders pdf is also well worth a read.

the hare said:

I run similar simulations on an ongoing basis, in order to try to work out statistical limits that I'm typically going to experience over the coming month. I tend to use resampling rather than true monte carlo

The Larry Sanders pdf is also well worth a read.

Click to expand...

Dear Hare,

Thank you for your reply. Could you kindly explain to the uninitiated the difference between 'resampling' vs 'true monte carlo'? Thanks,

fastcar

P.S.

I'm continuing to read Larry's paper, and it is the first time I have read anything that would help to explain why scalpers can do very well in the markets with high winning percentage systems, even if they have 'upside-down' win/loss ratios...

For example, I know two people who scalp, with win rates in the 90% range, while risking 3 times what they hope to make and these people do a ton of trades, and make a lot of money 4 out of 5 days a week, or better. I have never been comfortable with this approach, and don't know if I ever will be, but for the first time I'm starting to understand why it can work.

Check out the attachment. I have created yet another system, system 'C' that has an Expectancy of .2R. But it has a win rate of 90%, with a very poor Win/Loss ratio of .33 (it's losers are three times the size of it's winners) Compare this one to the earlier systems I snap shot, systems 'A' and 'B'.

Incredibly, THIS SYSTEM TOLERATES A 5% POSITION SIZE with the same risk of ruin as the previous two systems... Imagine how much more money it could make, than system 'B', using 6.5 times the leverage! I don't know how to use this yet, but It's really opening my eyes. I consider larry's paper to be a must read for every trader.

fastcar

fastcar said:

Dear Hare,

Thank you for your reply. Could you kindly explain to the uninitiated the difference between 'resampling' vs 'true monte carlo'? Thanks,

Click to expand...

I probably need to read up on this again becaue its been a while since I last looked, but if I recall correctly in a true monte carlo simulation, the analysis that is undertaken is based on an artificially generated sample population. This artificially generated popluation is based on statistics inferred from your actual trade results.

In resampling, you are repeatedly picking individual trades at random (with replacement) from the population of actual trade results. In simple terms assume each trade result is written on a piece of paper, and those bits of paper are placed in a bucket. To generate a random equity curve you pick out a result from the bucket, record it, then put the paper back in the bucket, and repeat N times.

I guess what I'm saying is that in monte carlo, you get to decide what the theoretical sample distribution is, but in resampling, the distribution is whatever it actually is warts and all.

The differences between the two approaches are discussed in David Aaronsons book "Evidence based technical analysis", and I remember writing code for both approaches, but coming down in favour of the resampling method (I cant really remember why, its a few years since I did this stuff)

fastcar,..Thanks for the responses. I will check out the pdf you sent. I guess I need to reread Van Tharps info on trading stats. I see your point on Win:Loss ratio. It really does make a difference. I need to understand these terms a bit more so i will read and post what I come up with. I have read the first part of Van Tharp's "Defnitive Guide..." but found it difficult and dry. I have not finished it yet but maybe I need to get a move on this. I just purchased Aronson's Book on Amazon.com.

Thanks

eegozi said:

fastcar,..Thanks for the responses. I will check out the pdf you sent. I guess I need to reread Van Tharps info on trading stats. I see your point on Win:Loss ratio. It really does make a difference. I need to understand these terms a bit more so i will read and post what I come up with. I have read the first part of Van Tharp's "Defnitive Guide..." but found it difficult and dry. I have not finished it yet but maybe I need to get a move on this. I just purchased Aronson's Book on Amazon.com.

Thanks

Click to expand...

eegozi, you may find Sanders treatment of money management more useful and practical than Van Tharp's. Van's chapter on Position Sizing in 'Super Trader' was quite readable, but did not solve any problems: he just proves that it's critical, and basically the chapter is a lead in to his special report 'The Definitive Guide to Position Sizing', which doesn't solve any problems, because you need software to model any of his ideas, and for reasons that are lost on me he won't provide the software (maybe liability?)

Van Tharp's main contribution to the discussion may be the idea of using R multiples to quantify Expectancy, rather than just a dollar amount. I skimmed the 'Definitive Guide' and focused on sections that were relevant to me, not areas I'd never use, e.g. portfolio related items, etc.

If you think Van is dry, have you looked inside Aronson's book at Amazon? I think it's even more technical. You may also want to check the table of contents. Besides the idea The Hare got out of it for using 'resampling' for his MC simulations, I'm not too sure how much content Aronsons book will have that relates to money management or, as Van calls it 'position sizing'. None of the chapters explicitly deal with this subject. The book seems to be related only to Technical Analysis, and applying the scientific method to it in a strict fashion.

I'll post anything worthy as I continue to trudge through Sander's paper.

fastcar

For position sizing and MM Simulations, this software isnt bad, and IIRC theres a demo version

http://adaptrade.com/MSA/index.htm

The software handles most of the models in tharps MM report.

fastcar said:

eegozi, you may find Sanders treatment of money management more useful and practical than Van Tharp's. Van's chapter on Position Sizing in 'Super Trader' was quite readable, but did not solve any problems: he just proves that it's critical, and basically the chapter is a lead in to his special report 'The Definitive Guide to Position Sizing', which doesn't solve any problems, because you need software to model any of his ideas, and for reasons that are lost on me he won't provide the software (maybe liability?)

Van Tharp's main contribution to the discussion may be the idea of using R multiples to quantify Expectancy, rather than just a dollar amount. I skimmed the 'Definitive Guide' and focused on sections that were relevant to me, not areas I'd never use, e.g. portfolio related items, etc.

If you think Van is dry, have you looked inside Aronson's book at Amazon? I think it's even more technical. You may also want to check the table of contents. Besides the idea The Hare got out of it for using 'resampling' for his MC simulations, I'm not too sure how much content Aronsons book will have that relates to money management or, as Van calls it 'position sizing'. None of the chapters explicitly deal with this subject. The book seems to be related only to Technical Analysis, and applying the scientific method to it in a strict fashion.

I'll post anything worthy as I continue to trudge through Sander's paper.

fastcar

Click to expand...

Thanks,...I just reread Supertrader for 4th time and setting up Excel to data mine. As for Aronson's book on Amazon,...well,..I bought it already. If it sucks it will just go on the shelf with the rest. Never can have too much information,... Its what you do with it that counts. I am also working on Sanders paper but I have just started. I'll keep you informed.

Preliminary info on my latest system data looks very promising!!

the hare said:

For position sizing and MM Simulations, this software isnt bad, and IIRC theres a demo version

Money management software :: Market System Analyzer

The software handles most of the models in tharps MM report.

Click to expand...

This looks very promising, hare - thanks so much for the recommendation!!!
These are the kind of solutions we need...

fastcar

eegozi said:

...Preliminary info on my latest system data looks very promising!!

Click to expand...

Sounds like you are a systems trader. I am a rules based discretionary trader. I look forward to collecting data on my setups, as well.

fastcar

fastcar said:

Sounds like you are a systems trader. I am a rules based discretionary trader. I look forward to collecting data on my setups, as well.

fastcar

Click to expand...

I guess I call it a system,..but it is more a rules based discretionary system. I do not take every trade the "system" says to take. I use my discretion and focus on areas (stocks and ETFs) that meet my parameters.

The more I read Sander's paper, the more my eyes open. Don't stop when you get to the explanation of how to use his software, keep plodding through. Their are gems throughout, for example page 54!

fastcar

Hello Guys,

Thanks for finally making this thread alive! I am currently busy but hope to be able to come back with some input over the weekend, including posting the excel spreadsheet which I use for my MC Sim.

It's quite an important topic, as my trading also has progressed quite well from initially posting here, but currently I am being held in a quick drawdown.

Cheers,
Yuppie

Hello Guys,

Thanks first for all the valuable input here, special thanks to Fastcar for the link and explanation and eegozi for continuing the thread.

I was looking at the link Fastcar posted and experimented a little bit.
I agree that the plain 5% equity per trade was wrong and will eventually lead to a ruin.
I found out later that I misused the sheet I used for MC (I downloaded it on the net).

Please find the link here: Trading Simulation

To use the sheet correctly you will need to

1) add you starting equity in the first grey cell
2) add you winning percentage in the second grey cell
3) put 0% into the third grey cell (risk)
4) multiply your equity risk (in my case 5%) with your average win/average loss ratio and add it into the forth grey cell (in my case 5%*2.06 = 10.12%)
5) put your equity risk (in my case 5%) into the forth grey cell (in my case 5%)

The sheet defines "ruin" as loss of 50% of initial equity - this is also misleading, as you might think a 90% drawdown later might be a ruin, although you are still up on your initial equity (not defined as a ruin by the sheet).

With the stats indicated earlier, I end up with a 35% "ruin" rate (defined as loss of 50% initial equity) with 1000 iterations on simulations with 1000 trades each.

Since my posting, thankfully, my P&L further improved, I reduced my initial risk vs. equity while still having doubled my average position size. My stats are currently the following:

Win Pct 39.75%
Lose Pct 60.25%
Av Win/Av Loss: 1.72

I am currently running about 2% initial equity risk on each position I enter.

However, and here comes my question: the actual risk I am running in each position shouldn't it rather be the AVERAGE loss of each losing trade than the initial equity risk taken?
I am a discretionary trader and I set stops according to the market, meaning I often immediately adjust stops when my position goes in my way, reducing the AVERAGE loss on losing positions to about 1% of equity. Any opinions ?

Some more questions:

@ fastcar: could you please help me with the explanations of your link? I put in my current stats and received the following:

Prob. Win: 0.40
Win/Loss ratio: 1.72
Risk Amt (%): 2
Number of periods: 10000
Risk of:
Loss level (%): 70
iteration: 1000 /1000

Risk (MC): 0.8% {is this the variance of the MC Sim?}
Risk of Ruin (formula): 3.15% {Is this my probability of a 70% drawdown?}


@ the hare: regarding re-sampling, do you think it is suitable if you keep your risk fixed to the total equity? Wouldn't that be erratic if you equity grows and you sample larger trade sizes randomly at the beginning ?

Here is also my current 2011 P&L Image - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting

This is on about 1800 trades so far, net of spreads/commissions; as said I am trading completely discrationary mainly in gold, oil, European Indices and some single stocks on an intraday or 1-3 day basis.

More input and reads regarding position sizing are more than welcome!

Thanks and have a good weekend,
Yuppie

Yuppie,

I dont know how you are getting such good results with your system if you have a ~40 win rate. If you win 1.72R * 40 trades = 6.88R when you win. If you lose 1R * 60 = 6R when you lose. Therefore over 100 trades you should net 0.88R. If you risk lets say,... 2% (as a normal commonly accepted maximum risk/trade). Then you should have a MAXIMUM gain of 2 * 0.88 = 1.76% gain in 100 trades. In reality it does not usually work that well. Thats where MC Sim helps. I ran your numbers in the MC Sim posted above and here is a screen shot. I did 1000 simulations and came up with a HIGH P&L of + $8872 and and LOW P&L of -$3640. This seems ok but not great. You also have a significant chance of losing money with this system based on the equity curve. See the attached pic.

Lastly, trading this system in a MC Sim makes it SEEM like a 100% mechanical system. However, you are trading a discretionary system and no matter how well you try to control your emotions when you have a losing streak your system will NOT function like the mechanical system and you will likely fall more toward the LOW P&L. It seems to me you need to improve your win probability somehow as when Ii entered 30.8% win rate in this same MC Sim I got a NEGATIVE expectancy.

The only thing I changed is that I used $7 as the commission charge because it seems you did not add that in as an expense and risk when you trade. If your commision is less let me know and try it on the MC Sim.

Yuppie13 said:

I am currently running about 2% initial equity risk on each position I enter.

However, and here comes my question: the actual risk I am running in each position shouldn't it rather be the AVERAGE loss of each losing trade than the initial equity risk taken?
I am a discretionary trader and I set stops according to the market, meaning I often immediately adjust stops when my position goes in my way, reducing the AVERAGE loss on losing positions to about 1% of equity. Any opinions ?

Click to expand...

I don't understand the question. You seem to be mixing your R-multiple distribution up with initial risk. R is ALWAYS your initial risk on a position. Just because you get to tighten your stops on some trades, doesn't mean anything. Why? Because you never want R to be more than your risk tolerance, in this case 2%.

If your tighter stop gets tapped, and you only lose 1% on that trade, that trade registers a -.5R, instead of a full -1R. That is fine, so long as you stuck to your rules about trailing stops.

I think you are over-thinking this part a bit. Just use 2% (if that meets your objective in connection with your risk tolerance), and keep moving stops according to plan.

Some more questions:

@ fastcar: could you please help me with the explanations of your link? I put in my current stats and received the following:

Prob. Win: 0.40
Win/Loss ratio: 1.72
Risk Amt (%): 2
Number of periods: 10000
Risk of:
Loss level (%): 70
iteration: 1000 /1000

Risk (MC): 0.8% {is this the variance of the MC Sim?}
Risk of Ruin (formula): 3.15% {Is this my probability of a 70% drawdown?}

Click to expand...

It means with a 40% win rate and a win/loss ratio of 1.72, risking 2% of your equity on each trade, after 1000 Monte Carlo simulations that include 10,000 trades each your RISK OF RUIN (70%) threshold is .8% and 3.15% respectively, as calculated using the simulator. PLEASE UNDERSTAND RISK OF RUIN IS USELESS, BECAUSE IT IS CALCULATED BASED ON YOUR INITIAL CAPITAL AND ALWAYS TENDS TOWARD ZERO AS YOU ADD MORE TRADES.

For example, you start with 10,000, and are willing to lose 70% of it down to $3000. The first string of trades ARE THE ONLY ONES THAT COUNT because as your equity grows, your chances of drawing down that deep are slim to none. So, lets say you make it to $15,000 - now you would need a an 80% percent draw down to ruin. If you make it to $30,000 you would need a 90% drawdown to ruin. I HOPE YOU CAN SEE HOW LITTLE USE THIS CALCULATION IS WITH RESPECT TO YOUR ONGOING POSITION SIZING STRATEGY. You need to focus on DRAWDOWN as reported by the MC simulations, and determine what your risk tolerance is. I have only come to understand this very well in the last week. I hope this is helpful to you.

@ the hare: regarding re-sampling, do you think it is suitable if you keep your risk fixed to the total equity? Wouldn't that be erratic if you equity grows and you sample larger trade sizes randomly at the beginning ?

Click to expand...

I look forward to Hare's input here, but thought I would chime in in case he was tied up: Hare was stating that he uses actual trade results in his MC simulations. This is preferable to the Marble Game, which used fixed R-multiples. In real life, you get many, many results, not just -1R, +1R, +2R etc. This was not emphasized at all by Van Tharp in 'The Definitive Guide to Position Sizing', which cannot be definitive since it leaves more questions than it answers.

Here is also my current 2011 P&L Image - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting

This is on about 1800 trades so far, net of spreads/commissions; as said I am trading completely discrationary mainly in gold, oil, European Indices and some single stocks on an intraday or 1-3 day basis.

More input and reads regarding position sizing are more than welcome!

Thanks and have a good weekend,
Yuppie

Click to expand...

Your trading is going very well. Are you live trading yet? If so, are you keeping track of your efficiency? Van Tharp writes about this in Super Trader, and I think next to position sizing, it's the most important aspect of trading. He states you must be trading at 90% efficiency (1 mistake in 10 - no more than that) to succeed in the long run. Your results appear to evidence good efficiency.

With respect to position sizing I would be very careful with a system that has only 40% winners. Based on 1000 simulations, and 500 trades per year, in a given year your chances of hitting a 50% drawdown are around 62% at 2% risk!!! Would you really be able to stomach that kind of loss? Would it effect your efficiency levels? Many people who experience that much pain begin revenge trading, or taking profits early, or skipping good trades due to fear, etc. and destroy an otherwise good system. You need to give this very careful consideration.

If you back down to 1% risk, your chances of a 50% drawdown are 0% on 500 trades and only 5% for a 33% drawdown (which is still sizable). If it were my account, I'd be using no more than 1%.

If you want more size, without experiencing devastating drawdowns, develop a system with a higher winning percentage. A system with a higher win rate even with a lower win/loss ratio will have a MUCH smoother equity curve, and allow you to safely use more leverage. Go on the simulator and play with a few systems, and see for yourself how much leverage they allow you to use for a given drawdown. This was the Gem I took from Larry C. Sanders white paper. This is something Sanders elucidated, but is lost on Van Tharp. Tharp believes it's ALL ABOUT EXPECTANCY and that you MUST keep losses small, and let winners run. But computer simulations clearly show that a system with a HIGHER WIN RATE, even IF it has a lower win/loss ratio, even if it has a LOWER EXPECTANCY will outperform. Why? Because you can safely use more leverage, and still meet your risk objectives.

Sanders work is the most sensible and comprehensive explanation to position sizing I have come across. In fact, I have so much confidence in his work, that I am no longer studying the subject. (The only thing that would incite me to do further research would be if I were trading a portfolio, rather than taking one trade at a time - which is what his work is based on) Not only does he explain everything you need to know (he even debunks 'optimal-f') but he provides software to do it. His white paper and software put to shame Van Tharp's 'Definitive Guide to Position Sizing' - which leaves the reader completely frustrated, since it leaves the reader with questions as well as offers no clear way to computer model what he discusses.

fastcar

eegozi said:

Yuppie,

I dont know how you are getting such good results with your system if you have a ~40 win rate. If you win 1.72R * 40 trades = 6.88R when you win. If you lose 1R * 60 = 6R when you lose. Therefore over 100 trades you should net 0.88R. If you risk lets say,... 2% (as a normal commonly accepted maximum risk/trade). Then you should have a MAXIMUM gain of 2 * 0.88 = 1.76% gain in 100 trades.

Click to expand...

eegozi,

I agree with everything you stated excepting the above. You calculate expectancy correctly (.88R), but that expectancy would be multiplied by his risk of 2% PER TRADE. That means he would grow his account by 1.76% PER TRADE in a perfect world, not per 100 trades as you state.

Kind Regards,

fastcar